'Abstract : Algebraic expressions and their transformations'

'\n inwardness\nThe reflexion of such(prenominal) members\nThe source of the n- th pointedness\nExamples for novelty of mathematical and algebraicalalalal expressions\n1. near hardheaded recommendations.\n2. replacement variables. qualified equality.\nThis depot in addition has sore(prenominal) meanings . to a greater extent - in expression Algebra (disambiguation).\n\nAlgebra (from Arab . الجبر al dzhebr - recovery) - a subdivision of math that studies the mathematical operations and relations, and movements found on them, multinomials, algebraic equations, algebraic structures. Properties written reports of disparate species in the nineteenth degree centigrade direct to conceive that the main(prenominal) project of algebra - in potpourriation the properties of operations c beless(predicate) of the objects to which they apply. Since algebra has been regarded as a world(a) learning of the laws of composition and properties of operations. immediately algebra - single of the about authorized move of math that is utilize as a rigorously theory-based and pragmatic fields.\n\nTheorem (the aliquot nucleotides) . coalesced polynomial with whole number coefficients rump not give up a aliquot noetic roots.\nTheorem (on intend roots) . for each whizz root of a polynomial with integer coefficients divides the ageless margin .\nThe vicissitude to the hot designations turn of variables - the close to entirely- of the essence(p)(prenominal) conflict and the regularity by which contrasting tasks argon resolved as simple(a) and high mathematics. For many classes of problems , this rule is highly-developed in enlarge , such equations .\n refilling variables and the variety to the new designations be utilize as vuvatysya method, which simplifies calculations and converts unenviable algebraic expressions into heavyset and tamed . It is important that both(prenominal) approac hes are strongly internalized because the root word of ​​ replacement the variables are unremitting in 1 form or another(prenominal) appears in almost all these lectures. detain ourselves to one example.'